Solve by substitution
-7x + y=1
7x- 6y =-6
from 1st eqn ... y - 1 = 7x
substitute for 7x in the 2nd equation
Step 1:
Solve -7x + y = 1 for y.
Do this by adding 7x to both sides.
-7x + y + 7x = 1 + 7x
y = 7x + 1
Step 2: Substitute 7x + 1 for y in 7x - 6y = -6
7x - 6y = -6
7x - 6(7x + 1) = -6
-35x - 6 = -6
-35x - 6 + 6 = -6 + 6
-35x = 0
-35x / -35 = 0 / -35
X = 0.
Step 3: Substitute 0 for x in y = 7x + 1 (the original equation.
y = 7x + 1
y = 7(0) + 1
Y = 1
Therefore x = 0 and y = 1
-7x + y=1
7x- 6y =-6
add the two equations, and the x vanishes, leaving
-5y = -5
y = 1
as above
To solve the system of equations by substitution, we isolate one variable in one equation and substitute it into the other equation. Let's solve these equations step-by-step:
1. Start with the given system of equations:
-7x + y = 1 (Equation 1)
7x - 6y = -6 (Equation 2)
2. Solve Equation 1 for y:
y = 7x + 1 (Equation 3)
3. Substitute Equation 3 into Equation 2:
7x - 6(7x + 1) = -6
7x - 42x - 6 = -6
4. Combine like terms:
-35x - 6 = -6
5. Move the constant term to the right side:
-35x = 0
6. Divide both sides by -35:
x = 0
7. Substitute the value of x back into Equation 3 to find y:
y = 7(0) + 1
y = 1
8. The solution to the system of equations is x = 0 and y = 1.
Therefore, the solution to the system of equations -7x + y = 1 and 7x - 6y = -6 is x = 0 and y = 1.